LMFDB - Embedded newform 197.6.b.a.196.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,6,Mod(196,197)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("197.196");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$197$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	197.b (of order $2$ , degree $1$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$31.5956125032$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			196.13
Character	$\chi$	$=$	197.196
Dual form			197.6.b.a.196.70

$q$ -expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.43577i q^{2} +1.06070i q^{3} -39.1622 q^{4} +26.8901i q^{5} +8.94786 q^{6} -197.867 q^{7} +60.4188i q^{8} +241.875 q^{9} +226.839 q^{10} -206.312i q^{11} -41.5395i q^{12} +993.628i q^{13} +1669.16i q^{14} -28.5224 q^{15} -743.512 q^{16} +433.577i q^{17} -2040.40i q^{18} +1019.16 q^{19} -1053.08i q^{20} -209.879i q^{21} -1740.40 q^{22} +805.905 q^{23} -64.0865 q^{24} +2401.92 q^{25} +8382.02 q^{26} +514.309i q^{27} +7748.91 q^{28} +2198.70 q^{29} +240.609i q^{30} -8257.98i q^{31} +8205.50i q^{32} +218.836 q^{33} +3657.56 q^{34} -5320.66i q^{35} -9472.36 q^{36} +13187.4 q^{37} -8597.41i q^{38} -1053.95 q^{39} -1624.67 q^{40} -7483.36 q^{41} -1770.49 q^{42} -10641.7 q^{43} +8079.63i q^{44} +6504.04i q^{45} -6798.43i q^{46} +17930.0 q^{47} -788.647i q^{48} +22344.4 q^{49} -20262.1i q^{50} -459.898 q^{51} -38912.7i q^{52} +34590.8 q^{53} +4338.59 q^{54} +5547.74 q^{55} -11954.9i q^{56} +1081.03i q^{57} -18547.7i q^{58} +10659.1 q^{59} +1117.00 q^{60} -39077.4 q^{61} -69662.4 q^{62} -47859.1 q^{63} +45427.3 q^{64} -26718.7 q^{65} -1846.05i q^{66} +4190.27i q^{67} -16979.9i q^{68} +854.827i q^{69} -44883.9 q^{70} +29284.3i q^{71} +14613.8i q^{72} -14285.1i q^{73} -111246. i q^{74} +2547.73i q^{75} -39912.6 q^{76} +40822.3i q^{77} +8890.85i q^{78} -42387.9i q^{79} -19993.1i q^{80} +58230.1 q^{81} +63127.9i q^{82} +852.050 q^{83} +8219.31i q^{84} -11658.9 q^{85} +89771.1i q^{86} +2332.17i q^{87} +12465.1 q^{88} +126382. i q^{89} +54866.5 q^{90} -196606. i q^{91} -31561.0 q^{92} +8759.28 q^{93} -151253. i q^{94} +27405.3i q^{95} -8703.61 q^{96} +85204.5 q^{97} -188492. i q^{98} -49901.7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$82 q - 1272 q^{4} + 56 q^{6} - 294 q^{7} - 6644 q^{9} + 1162 q^{10} - 122 q^{15} + 13088 q^{16} + 738 q^{19} + 6534 q^{22} - 456 q^{23} - 446 q^{24} - 45670 q^{25} - 2380 q^{26} + 21660 q^{28} + 2052 q^{29}+ \cdots - 395422 q^{97}+O(q^{100})$ 82 * q - 1272 * q^4 + 56 * q^6 - 294 * q^7 - 6644 * q^9 + 1162 * q^10 - 122 * q^15 + 13088 * q^16 + 738 * q^19 + 6534 * q^22 - 456 * q^23 - 446 * q^24 - 45670 * q^25 - 2380 * q^26 + 21660 * q^28 + 2052 * q^29 + 8068 * q^33 - 29612 * q^34 + 98540 * q^36 + 4182 * q^37 - 56242 * q^39 - 14880 * q^40 + 6074 * q^41 - 52390 * q^42 + 47302 * q^43 - 32854 * q^47 + 234940 * q^49 + 38010 * q^51 + 9186 * q^53 - 88518 * q^54 - 72930 * q^55 + 150142 * q^59 + 67874 * q^60 - 118558 * q^61 + 176982 * q^62 + 112446 * q^63 - 35834 * q^64 - 5434 * q^65 - 38102 * q^70 - 42536 * q^76 + 634854 * q^81 - 437360 * q^83 + 291628 * q^85 - 88678 * q^88 - 408654 * q^90 + 175588 * q^92 - 449962 * q^93 - 41002 * q^96 - 395422 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		−	8.43577i		−	1.49125i	−0.666367	−	0.745624i	$-0.732152\pi$
$2$		−	8.43577i		−	1.49125i	0.666367	−	0.745624i	$-0.267848\pi$
$3$			1.06070i			0.0680442i	0.999421	+	0.0340221i	$0.0108317\pi$
$3$			1.06070i			0.0680442i	−0.999421	+	0.0340221i	$0.989168\pi$
$4$	−39.1622			−1.22382
$5$			26.8901i			0.481024i	0.970646	+	0.240512i	$0.0773154\pi$
$5$			26.8901i			0.481024i	−0.970646	+	0.240512i	$0.922685\pi$
$6$	8.94786			0.101471
$7$	−197.867			−1.52626			−0.763130	−	0.646245i	$-0.776338\pi$
$7$	−197.867			−1.52626			−0.763130	+	0.646245i	$0.776338\pi$
$8$			60.4188i			0.333770i
$9$	241.875			0.995370
$10$	226.839			0.717326
$11$		−	206.312i		−	0.514094i	−0.966399	−	0.257047i	$-0.917250\pi$
$11$		−	206.312i		−	0.514094i	0.966399	−	0.257047i	$-0.0827495\pi$
$12$		−	41.5395i		−	0.0832739i
$13$			993.628i			1.63067i	0.578991	+	0.815334i	$0.303447\pi$
$13$			993.628i			1.63067i	−0.578991	+	0.815334i	$0.696553\pi$
$14$			1669.16i			2.27603i
$15$	−28.5224			−0.0327309
$16$	−743.512			−0.726086
$17$			433.577i			0.363868i	0.983311	+	0.181934i	$0.0582358\pi$
$17$			433.577i			0.363868i	−0.983311	+	0.181934i	$0.941764\pi$
$18$		−	2040.40i		−	1.48434i
$19$	1019.16			0.647678			0.323839	−	0.946112i	$-0.395026\pi$
$19$	1019.16			0.647678			0.323839	+	0.946112i	$0.395026\pi$
$20$		−	1053.08i		−	0.588687i
$21$		−	209.879i		−	0.103853i
$22$	−1740.40			−0.766641
$23$	805.905			0.317661			0.158831	−	0.987306i	$-0.449228\pi$
$23$	805.905			0.317661			0.158831	+	0.987306i	$0.449228\pi$
$24$	−64.0865			−0.0227111
$25$	2401.92			0.768616
$26$	8382.02			2.43173
$27$			514.309i			0.135773i
$28$	7748.91			1.86787
$29$	2198.70			0.485479			0.242739	−	0.970092i	$-0.421954\pi$
$29$	2198.70			0.485479			0.242739	+	0.970092i	$0.421954\pi$
$30$			240.609i			0.0488099i
$31$		−	8257.98i		−	1.54337i	−0.636006	−	0.771684i	$-0.719415\pi$
$31$		−	8257.98i		−	1.54337i	0.636006	−	0.771684i	$-0.280585\pi$
$32$			8205.50i			1.41654i
$33$	218.836			0.0349811
$34$	3657.56			0.542618
$35$		−	5320.66i		−	0.734168i
$36$	−9472.36			−1.21815
$37$	13187.4			1.58363			0.791816	−	0.610759i	$-0.209136\pi$
$37$	13187.4			1.58363			0.791816	+	0.610759i	$0.209136\pi$
$38$		−	8597.41i		−	0.965848i
$39$	−1053.95			−0.110958
$40$	−1624.67			−0.160551
$41$	−7483.36			−0.695243			−0.347622	−	0.937635i	$-0.613011\pi$
$41$	−7483.36			−0.695243			−0.347622	+	0.937635i	$0.613011\pi$
$42$	−1770.49			−0.154871
$43$	−10641.7			−0.877689			−0.438844	−	0.898563i	$-0.644612\pi$
$43$	−10641.7			−0.877689			−0.438844	+	0.898563i	$0.644612\pi$
$44$			8079.63i			0.629158i
$45$			6504.04i			0.478797i
$46$		−	6798.43i		−	0.473712i
$47$	17930.0			1.18396			0.591978	−	0.805954i	$-0.298347\pi$
$47$	17930.0			1.18396			0.591978	+	0.805954i	$0.298347\pi$
$48$		−	788.647i		−	0.0494060i
$49$	22344.4			1.32947
$50$		−	20262.1i		−	1.14620i
$51$	−459.898			−0.0247592
$52$		−	38912.7i		−	1.99564i
$53$	34590.8			1.69150			0.845748	−	0.533583i	$-0.179155\pi$
$53$	34590.8			1.69150			0.845748	+	0.533583i	$0.179155\pi$
$54$	4338.59			0.202472
$55$	5547.74			0.247292
$56$		−	11954.9i		−	0.509419i
$57$			1081.03i			0.0440707i
$58$		−	18547.7i		−	0.723969i
$59$	10659.1			0.398649			0.199325	−	0.979934i	$-0.436125\pi$
$59$	10659.1			0.398649			0.199325	+	0.979934i	$0.436125\pi$
$60$	1117.00			0.0400568
$61$	−39077.4			−1.34463			−0.672313	−	0.740267i	$-0.734699\pi$
$61$	−39077.4			−1.34463			−0.672313	+	0.740267i	$0.734699\pi$
$62$	−69662.4			−2.30154
$63$	−47859.1			−1.51919
$64$	45427.3			1.38633
$65$	−26718.7			−0.784391
$66$		−	1846.05i		−	0.0521655i
$67$			4190.27i			0.114039i	0.998373	+	0.0570197i	$0.0181598\pi$
$67$			4190.27i			0.114039i	−0.998373	+	0.0570197i	$0.981840\pi$
$68$		−	16979.9i		−	0.445309i
$69$			854.827i			0.0216150i
$70$	−44883.9			−1.09483
$71$			29284.3i			0.689427i	0.938708	+	0.344714i	$0.112024\pi$
$71$			29284.3i			0.689427i	−0.938708	+	0.344714i	$0.887976\pi$
$72$			14613.8i			0.332224i
$73$		−	14285.1i		−	0.313745i	−0.987619	−	0.156872i	$-0.949859\pi$
$73$		−	14285.1i		−	0.313745i	0.987619	−	0.156872i	$-0.0501412\pi$
$74$		−	111246.i		−	2.36159i
$75$			2547.73i			0.0522999i
$76$	−39912.6			−0.792640
$77$			40822.3i			0.784641i
$78$			8890.85i			0.165465i
$79$		−	42387.9i		−	0.764141i	−0.924133	−	0.382071i	$-0.875211\pi$
$79$		−	42387.9i		−	0.764141i	0.924133	−	0.382071i	$-0.124789\pi$
$80$		−	19993.1i		−	0.349265i
$81$	58230.1			0.986131
$82$			63127.9i			1.03678i
$83$	852.050			0.0135759			0.00678797	−	0.999977i	$-0.497839\pi$
$83$	852.050			0.0135759			0.00678797	+	0.999977i	$0.497839\pi$
$84$			8219.31i			0.127098i
$85$	−11658.9			−0.175030
$86$			89771.1i			1.30885i
$87$			2332.17i			0.0330340i
$88$	12465.1			0.171589
$89$			126382.i			1.69125i	0.533775	+	0.845626i	$0.320773\pi$
$89$			126382.i			1.69125i	−0.533775	+	0.845626i	$0.679227\pi$
$90$	54866.5			0.714005
$91$		−	196606.i		−	2.48882i
$92$	−31561.0			−0.388760
$93$	8759.28			0.105017
$94$		−	151253.i		−	1.76557i
$95$			27405.3i			0.311549i
$96$	−8703.61			−0.0963876
$97$	85204.5			0.919461			0.459730	−	0.888059i	$-0.347946\pi$
$97$	85204.5			0.919461			0.459730	+	0.888059i	$0.347946\pi$
$98$		−	188492.i		−	1.98257i
$99$		−	49901.7i		−	0.511714i
$100$	−94064.6			−0.940646
$101$	−20688.5			−0.201802			−0.100901	−	0.994896i	$-0.532173\pi$
$101$	−20688.5			−0.201802			−0.100901	+	0.994896i	$0.532173\pi$
$102$			3879.59i			0.0369220i
$103$			83994.0i			0.780109i	0.920792	+	0.390054i	$0.127544\pi$
$103$			83994.0i			0.780109i	−0.920792	+	0.390054i	$0.872456\pi$
$104$	−60033.8			−0.544267
$105$	5643.65			0.0499559
$106$		−	291800.i		−	2.52244i
$107$	−13758.2			−0.116172			−0.0580861	−	0.998312i	$-0.518500\pi$
$107$	−13758.2			−0.116172			−0.0580861	+	0.998312i	$0.518500\pi$
$108$		−	20141.5i		−	0.166162i
$109$	70128.2			0.565361			0.282681	−	0.959214i	$-0.408776\pi$
$109$	70128.2			0.565361			0.282681	+	0.959214i	$0.408776\pi$
$110$		−	46799.5i		−	0.368773i
$111$			13987.9i			0.107757i
$112$	147117.			1.10820
$113$			193933.i			1.42875i	0.699763	+	0.714375i	$0.253289\pi$
$113$			193933.i			1.42875i	−0.699763	+	0.714375i	$0.746711\pi$
$114$	9119.31			0.0657204
$115$			21670.9i			0.152803i
$116$	−86105.8			−0.594138
$117$			240334.i			1.62312i
$118$		−	89917.8i		−	0.594485i
$119$		−	85790.7i		−	0.555358i
$120$		−	1723.29i		−	0.0109246i
$121$	118486.			0.735707
$122$			329648.i			2.00517i
$123$		−	7937.63i		−	0.0473073i
$124$			323401.i			1.88880i
$125$			148619.i			0.850747i
$126$			403728.i			2.26549i
$127$	260160.			1.43130			0.715651	−	0.698458i	$-0.246130\pi$
$127$	260160.			1.43130			0.715651	+	0.698458i	$0.246130\pi$
$128$		−	120638.i		−	0.650819i
$129$		−	11287.7i		−	0.0597217i
$130$			225393.i			1.16972i
$131$		−	166918.i		−	0.849815i	−0.905237	−	0.424907i	$-0.860307\pi$
$131$		−	166918.i		−	0.849815i	0.905237	−	0.424907i	$-0.139693\pi$
$132$	−8570.10			−0.0428106
$133$	−201659.			−0.988525
$134$	35348.1			0.170061
$135$	−13829.8			−0.0653103
$136$	−26196.2			−0.121448
$137$	236447.			1.07630			0.538150	−	0.842849i	$-0.319123\pi$
$137$	236447.			1.07630			0.538150	+	0.842849i	$0.319123\pi$
$138$	7211.13			0.0322334
$139$			307008.i			1.34776i	0.738840	+	0.673881i	$0.235374\pi$
$139$			307008.i			1.34776i	−0.738840	+	0.673881i	$0.764626\pi$
$140$			208369.i			0.898489i
$141$			19018.4i			0.0805614i
$142$	247035.			1.02811
$143$	204997.			0.838317
$144$	−179837.			−0.722724
$145$			59123.1i			0.233527i
$146$	−120506.			−0.467871
$147$			23700.8i			0.0904628i
$148$	−516447.			−1.93808
$149$			247037.i			0.911582i	0.890087	+	0.455791i	$0.150644\pi$
$149$			247037.i			0.911582i	−0.890087	+	0.455791i	$0.849356\pi$
$150$	21492.1			0.0779920
$151$		−	296422.i		−	1.05796i	−0.848635	−	0.528979i	$-0.822575\pi$
$151$		−	296422.i		−	1.05796i	0.848635	−	0.528979i	$-0.177425\pi$
$152$			61576.5i			0.216175i
$153$			104871.i			0.362184i
$154$	344368.			1.17009
$155$	222058.			0.742398
$156$	41274.9			0.135792
$157$	−6499.41			−0.0210438			−0.0105219	−	0.999945i	$-0.503349\pi$
$157$	−6499.41			−0.0210438			−0.0105219	+	0.999945i	$0.503349\pi$
$158$	−357574.			−1.13952
$159$			36690.6i			0.115097i
$160$	−220646.			−0.681392
$161$	−159462.			−0.484834
$162$		−	491215.i		−	1.47057i
$163$	−84724.6			−0.249770			−0.124885	−	0.992171i	$-0.539856\pi$
$163$	−84724.6			−0.249770			−0.124885	+	0.992171i	$0.539856\pi$
$164$	293065.			0.850852
$165$			5884.52i			0.0168268i
$166$		−	7187.70i		−	0.0202451i
$167$		−	46347.5i		−	0.128598i	−0.997931	−	0.0642992i	$-0.979519\pi$
$167$		−	46347.5i		−	0.128598i	0.997931	−	0.0642992i	$-0.0204812\pi$
$168$	12680.6			0.0346631
$169$	−616004.			−1.65908
$170$			98352.1i			0.261012i
$171$	246510.			0.644679
$172$	416753.			1.07413
$173$	194665.			0.494508			0.247254	−	0.968951i	$-0.420472\pi$
$173$	194665.			0.494508			0.247254	+	0.968951i	$0.420472\pi$
$174$	19673.6			0.0492619
$175$	−475262.			−1.17311
$176$			153395.i			0.373276i
$177$			11306.2i			0.0271258i
$178$	1.06613e6			2.52208
$179$		−	252851.i		−	0.589836i	−0.955523	−	0.294918i	$-0.904708\pi$
$179$		−	252851.i		−	0.589836i	0.955523	−	0.294918i	$-0.0952924\pi$
$180$		−	254712.i		−	0.585961i
$181$	270202.			0.613045			0.306523	−	0.951863i	$-0.400835\pi$
$181$	270202.			0.613045			0.306523	+	0.951863i	$0.400835\pi$
$182$	−1.65853e6			−3.71145
$183$		−	41449.6i		−	0.0914941i
$184$			48691.8i			0.106026i
$185$			354610.i			0.761766i
$186$		−	73891.3i		−	0.156607i
$187$	89452.2			0.187063
$188$	−702178.			−1.44895
$189$		−	101765.i		−	0.207226i
$190$	231185.			0.464596
$191$	351814.			0.697798			0.348899	−	0.937160i	$-0.386556\pi$
$191$	351814.			0.697798			0.348899	+	0.937160i	$0.386556\pi$
$192$			48185.0i			0.0943318i
$193$	−621190.			−1.20041			−0.600207	−	0.799845i	$-0.704915\pi$
$193$	−621190.			−1.20041			−0.600207	+	0.799845i	$0.704915\pi$
$194$		−	718765.i		−	1.37114i
$195$		−	28340.7i		−	0.0533733i
$196$	−875056.			−1.62703
$197$	−179533.	−	514273.i	−0.329594	−	0.944123i
$197$	−179533.	−	514273.i	−0.329594	−	0.944123i
$198$	−420959.			−0.763092
$199$			490961.i			0.878849i	0.898280	+	0.439424i	$0.144818\pi$
$199$			490961.i			0.878849i	−0.898280	+	0.439424i	$0.855182\pi$
$200$			145121.i			0.256541i
$201$	−4444.64			−0.00775972
$202$			174524.i			0.300937i
$203$	−435050.			−0.740967
$204$	18010.6			0.0303007
$205$		−	201228.i		−	0.334429i
$206$	708554.			1.16334
$207$	194928.			0.316191
$208$		−	738775.i		−	1.18401i
$209$		−	210265.i		−	0.332967i
$210$		−	47608.6i		−	0.0744967i
$211$			945254.i			1.46165i	0.682566	+	0.730824i	$0.260864\pi$
$211$			945254.i			1.46165i	−0.682566	+	0.730824i	$0.739136\pi$
$212$	−1.35465e6			−2.07008
$213$	−31062.0			−0.0469115
$214$			116061.i			0.173241i
$215$		−	286157.i		−	0.422190i
$216$	−31073.9			−0.0453171
$217$			1.63398e6i			2.35558i
$218$		−	591585.i		−	0.843094i
$219$	15152.3			0.0213485
$220$	−217262.			−0.302640
$221$	−430815.			−0.593349
$222$	117999.			0.160692
$223$	1.19123e6			1.60410			0.802052	−	0.597255i	$-0.203742\pi$
$223$	1.19123e6			1.60410			0.802052	+	0.597255i	$0.203742\pi$
$224$		−	1.62360e6i		−	2.16201i
$225$	580965.			0.765057
$226$	1.63598e6			2.13062
$227$			762546.i			0.982203i	0.871102	+	0.491102i	$0.163406\pi$
$227$			762546.i			0.982203i	−0.871102	+	0.491102i	$0.836594\pi$
$228$		−	42335.5i		−	0.0539346i
$229$		−	938568.i		−	1.18271i	−0.806412	−	0.591354i	$-0.798594\pi$
$229$		−	938568.i		−	1.18271i	0.806412	−	0.591354i	$-0.201406\pi$
$230$	182810.			0.227867
$231$	−43300.5			−0.0533903
$232$			132842.i			0.162038i
$233$	−1.21442e6			−1.46547			−0.732736	−	0.680513i	$-0.761757\pi$
$233$	−1.21442e6			−1.46547			−0.732736	+	0.680513i	$0.761757\pi$
$234$	2.02740e6			2.42047
$235$			482139.i			0.569512i
$236$	−417434.			−0.487875
$237$	44961.0			0.0519954
$238$	−723711.			−0.828176
$239$	−903839.			−1.02352			−0.511760	−	0.859128i	$-0.671006\pi$
$239$	−903839.			−1.02352			−0.511760	+	0.859128i	$0.671006\pi$
$240$	21206.8			0.0237655
$241$		−	606342.i		−	0.672474i	−0.941777	−	0.336237i	$-0.890846\pi$
$241$		−	606342.i		−	0.672474i	0.941777	−	0.336237i	$-0.109154\pi$
$242$		−	999524.i		−	1.09712i
$243$			186742.i			0.202874i
$244$	1.53036e6			1.64558
$245$			600843.i			0.639507i
$246$	−66960.0			−0.0705469
$247$			1.01267e6i			1.05615i
$248$	498937.			0.515130
$249$			903.774i			0.000923765i
$250$	1.25372e6			1.26867
$251$	−1.66375e6			−1.66688			−0.833439	−	0.552612i	$-0.813631\pi$
$251$	−1.66375e6			−1.66688			−0.833439	+	0.552612i	$0.813631\pi$
$252$	1.87427e6			1.85922
$253$		−	166268.i		−	0.163308i
$254$		−	2.19465e6i		−	2.13443i
$255$		−	12366.7i		−	0.0119098i
$256$	435996.			0.415799
$257$	974512.			0.920353			0.460176	−	0.887828i	$-0.347786\pi$
$257$	974512.			0.920353			0.460176	+	0.887828i	$0.347786\pi$
$258$	−95220.6			−0.0890598
$259$	−2.60935e6			−2.41704
$260$	1.04637e6			0.959953
$261$	531809.			0.483231
$262$	−1.40808e6			−1.26728
$263$		−	2.06818e6i		−	1.84373i	−0.387507	−	0.921867i	$-0.626664\pi$
$263$		−	2.06818e6i		−	1.84373i	0.387507	−	0.921867i	$-0.373336\pi$
$264$			13221.8i			0.0116756i
$265$			930149.i			0.813650i
$266$			1.70114e6i			1.47413i
$267$	−134053.			−0.115080
$268$		−	164100.i		−	0.139564i
$269$		−	338777.i		−	0.285452i	−0.989762	−	0.142726i	$-0.954413\pi$
$269$		−	338777.i		−	0.285452i	0.989762	−	0.142726i	$-0.0455867\pi$
$270$			116665.i			0.0973939i
$271$			1.89952e6i			1.57116i	0.618761	+	0.785579i	$0.287635\pi$
$271$			1.89952e6i			1.57116i	−0.618761	+	0.785579i	$0.712365\pi$
$272$		−	322370.i		−	0.264200i
$273$	208541.			0.169350
$274$		−	1.99462e6i		−	1.60503i
$275$		−	495545.i		−	0.395141i
$276$		−	33476.9i		−	0.0264529i
$277$		−	44785.0i		−	0.0350698i	−0.999846	−	0.0175349i	$-0.994418\pi$
$277$		−	44785.0i		−	0.0350698i	0.999846	−	0.0175349i	$-0.00558181\pi$
$278$	2.58985e6			2.00985
$279$		−	1.99740e6i		−	1.53622i
$280$	321468.			0.245043
$281$			903784.i			0.682808i	0.939917	+	0.341404i	$0.110902\pi$
$281$			903784.i			0.682808i	−0.939917	+	0.341404i	$0.889098\pi$
$282$	160435.			0.120137
$283$			1.27072e6i			0.943157i	0.881824	+	0.471579i	$0.156316\pi$
$283$			1.27072e6i			0.943157i	−0.881824	+	0.471579i	$0.843684\pi$
$284$		−	1.14684e6i		−	0.843734i
$285$	−29069.0			−0.0211991
$286$		−	1.72931e6i		−	1.25014i
$287$	1.48071e6			1.06112
$288$			1.98470e6i			1.40998i
$289$	1.23187e6			0.867600
$290$	498749.			0.348247
$291$			90376.8i			0.0625640i
$292$			559437.i			0.383967i
$293$	−455227.			−0.309784			−0.154892	−	0.987931i	$-0.549503\pi$
$293$	−455227.			−0.309784			−0.154892	+	0.987931i	$0.549503\pi$
$294$	199935.			0.134902
$295$			286624.i			0.191760i
$296$			796766.i			0.528568i
$297$	106108.			0.0698003
$298$	2.08394e6			1.35939
$299$			800770.i			0.518000i
$300$		−	99774.8i		−	0.0640056i
$301$	2.10565e6			1.33958
$302$	−2.50055e6			−1.57768
$303$		−	21944.4i		−	0.0137315i
$304$	−757759.			−0.470270
$305$		−	1.05080e6i		−	0.646798i
$306$	884672.			0.540106
$307$		−	885875.i		−	0.536446i	−0.963357	−	0.268223i	$-0.913564\pi$
$307$		−	885875.i		−	0.536446i	0.963357	−	0.268223i	$-0.0864365\pi$
$308$		−	1.59869e6i		−	0.960259i
$309$	−89092.8			−0.0530819
$310$		−	1.87323e6i		−	1.10710i
$311$	−611214.			−0.358338			−0.179169	−	0.983818i	$-0.557341\pi$
$311$	−611214.			−0.358338			−0.179169	+	0.983818i	$0.557341\pi$
$312$		−	63678.1i		−	0.0370343i
$313$	−1.90313e6			−1.09801			−0.549007	−	0.835818i	$-0.684994\pi$
$313$	−1.90313e6			−1.09801			−0.549007	+	0.835818i	$0.684994\pi$
$314$			54827.5i			0.0313816i
$315$		−	1.28693e6i		−	0.730769i
$316$			1.66000e6i			0.935171i
$317$		−	3.34581e6i		−	1.87005i	−0.354579	−	0.935026i	$-0.615376\pi$
$317$		−	3.34581e6i		−	1.87005i	0.354579	−	0.935026i	$-0.384624\pi$
$318$	309514.			0.171637
$319$		−	453617.i		−	0.249582i
$320$			1.22154e6i			0.666859i
$321$		−	14593.4i		−	0.00790485i
$322$			1.34519e6i			0.723007i
$323$			441885.i			0.235669i
$324$	−2.28042e6			−1.20685
$325$			2.38662e6i			1.25336i
$326$			714717.i			0.372469i
$327$			74385.3i			0.0384696i
$328$		−	452135.i		−	0.232051i
$329$	−3.54776e6			−1.80703
$330$	49640.4			0.0250929
$331$	−591756.			−0.296874			−0.148437	−	0.988922i	$-0.547424\pi$
$331$	−591756.			−0.296874			−0.148437	+	0.988922i	$0.547424\pi$
$332$	−33368.2			−0.0166145
$333$	3.18970e6			1.57630
$334$	−390977.			−0.191772
$335$	−112677.			−0.0548557
$336$			156047.i			0.0754064i
$337$		−	1.99851e6i		−	0.958586i	−0.877655	−	0.479293i	$-0.840893\pi$
$337$		−	1.99851e6i		−	0.958586i	0.877655	−	0.479293i	$-0.159107\pi$
$338$			5.19647e6i			2.47410i
$339$	−205706.			−0.0972183
$340$	456590.			0.214205
$341$	−1.70372e6			−0.793437
$342$		−	2.07950e6i		−	0.961376i
$343$	−1.09567e6			−0.502857
$344$		−	642959.i		−	0.292946i
$345$	−22986.4			−0.0103974
$346$		−	1.64215e6i		−	0.737434i
$347$	64208.1			0.0286264			0.0143132	−	0.999898i	$-0.495444\pi$
$347$	64208.1			0.0286264			0.0143132	+	0.999898i	$0.495444\pi$
$348$		−	91332.8i		−	0.0404277i
$349$		−	427503.i		−	0.187878i	−0.995578	−	0.0939390i	$-0.970054\pi$
$349$		−	427503.i		−	0.187878i	0.995578	−	0.0939390i	$-0.0299459\pi$
$350$			4.00920e6i			1.74939i
$351$	−511032.			−0.221401
$352$	1.69289e6			0.728237
$353$	1.32713e6			0.566860			0.283430	−	0.958993i	$-0.408528\pi$
$353$	1.32713e6			0.566860			0.283430	+	0.958993i	$0.408528\pi$
$354$	95376.2			0.0404513
$355$	−787456.			−0.331631
$356$		−	4.94938e6i		−	2.06979i
$357$	90998.6			0.0377889
$358$	−2.13299e6			−0.879592
$359$			2.77922e6i			1.13812i	0.822297	+	0.569059i	$0.192692\pi$
$359$			2.77922e6i			1.13812i	−0.822297	+	0.569059i	$0.807308\pi$
$360$	−392966.			−0.159808
$361$	−1.43741e6			−0.580514
$362$		−	2.27936e6i		−	0.914202i
$363$			125679.i			0.0500607i
$364$			7.69954e6i			3.04587i
$365$	384128.			0.150919
$366$	−349660.			−0.136440
$367$			5.07293e6i			1.96605i	0.183479	+	0.983024i	$0.441264\pi$
$367$			5.07293e6i			1.96605i	−0.183479	+	0.983024i	$0.558736\pi$
$368$	−599200.			−0.230649
$369$	−1.81004e6			−0.692024
$370$	2.99141e6			1.13598
$371$	−6.84438e6			−2.58166
$372$	−343033.			−0.128522
$373$			2.96807e6i			1.10459i	0.833648	+	0.552296i	$0.186248\pi$
$373$			2.96807e6i			1.10459i	−0.833648	+	0.552296i	$0.813752\pi$
$374$		−	754598.i		−	0.278957i
$375$	−157641.			−0.0578885
$376$			1.08331e6i			0.395169i
$377$			2.18469e6i			0.791654i
$378$	−858465.			−0.309025
$379$	268521.			0.0960240			0.0480120	−	0.998847i	$-0.484711\pi$
$379$	268521.			0.0960240			0.0480120	+	0.998847i	$0.484711\pi$
$380$		−	1.07325e6i		−	0.381279i
$381$			275953.i			0.0973919i
$382$		−	2.96782e6i		−	1.04059i
$383$		−	5.28753e6i		−	1.84186i	−0.389731	−	0.920929i	$-0.627432\pi$
$383$		−	5.28753e6i		−	1.84186i	0.389731	−	0.920929i	$-0.372568\pi$
$384$	127962.			0.0442845
$385$	−1.09772e6			−0.377432
$386$			5.24022e6i			1.79011i
$387$	−2.57396e6			−0.873625
$388$	−3.33680e6			−1.12525
$389$		−	2.21500e6i		−	0.742162i	−0.928600	−	0.371081i	$-0.878987\pi$
$389$		−	2.21500e6i		−	0.742162i	0.928600	−	0.371081i	$-0.121013\pi$
$390$	−239076.			−0.0795928
$391$			349422.i			0.115587i
$392$			1.35002e6i			0.443737i
$393$	177050.			0.0578250
$394$	−4.33829e6	+	1.51450e6i	−1.40792	+	0.491506i
$395$	1.13981e6			0.367571
$396$			1.95426e6i			0.626245i
$397$		−	292439.i		−	0.0931233i	−0.998915	−	0.0465617i	$-0.985174\pi$
$397$		−	292439.i		−	0.0931233i	0.998915	−	0.0465617i	$-0.0148264\pi$
$398$	4.14163e6			1.31058
$399$		−	213900.i		−	0.0672634i
$400$	−1.78586e6			−0.558081
$401$	−2.62872e6			−0.816364			−0.408182	−	0.912901i	$-0.633837\pi$
$401$	−2.62872e6			−0.816364			−0.408182	+	0.912901i	$0.633837\pi$
$402$			37493.9i			0.0115717i
$403$	8.20536e6			2.51672
$404$	810209.			0.246970
$405$			1.56581e6i			0.474353i
$406$			3.66998e6i			1.10496i
$407$		−	2.72071e6i		−	0.814136i
$408$		−	27786.4i		−	0.00826385i
$409$	−1.53249e6			−0.452991			−0.226495	−	0.974012i	$-0.572727\pi$
$409$	−1.53249e6			−0.452991			−0.226495	+	0.974012i	$0.572727\pi$
$410$	−1.69751e6			−0.498716
$411$			250801.i			0.0732360i
$412$		−	3.28939e6i		−	0.954712i
$413$	−2.10909e6			−0.608442
$414$		−	1.64437e6i		−	0.471518i
$415$			22911.7i			0.00653036i
$416$	−8.15321e6			−2.30991
$417$	−325645.			−0.0917074
$418$	−1.77375e6			−0.496537
$419$	−4.33352e6			−1.20588			−0.602942	−	0.797785i	$-0.706005\pi$
$419$	−4.33352e6			−1.20588			−0.602942	+	0.797785i	$0.706005\pi$
$420$	−221018.			−0.0611370
$421$		−	1.80292e6i		−	0.495760i	−0.968791	−	0.247880i	$-0.920266\pi$
$421$		−	1.80292e6i		−	0.495760i	0.968791	−	0.247880i	$-0.0797338\pi$
$422$	7.97395e6			2.17968
$423$	4.33682e6			1.17847
$424$			2.08993e6i			0.564570i
$425$			1.04142e6i			0.279675i
$426$			262031.i			0.0699567i
$427$	7.73214e6			2.05225
$428$	538801.			0.142174
$429$			217442.i			0.0570426i
$430$	−2.41395e6			−0.629589
$431$	4.98696e6			1.29313			0.646565	−	0.762859i	$-0.276205\pi$
$431$	4.98696e6			1.29313			0.646565	+	0.762859i	$0.276205\pi$
$432$		−	382395.i		−	0.0985832i
$433$	384528.			0.0985617			0.0492809	−	0.998785i	$-0.484307\pi$
$433$	384528.			0.0985617			0.0492809	+	0.998785i	$0.484307\pi$
$434$	1.37839e7			3.51276
$435$	−62712.2			−0.0158902
$436$	−2.74637e6			−0.691900
$437$	821347.			0.205742
$438$		−	127821.i		−	0.0318360i
$439$			4.14600e6i			1.02676i	0.858162	+	0.513379i	$0.171606\pi$
$439$			4.14600e6i			1.02676i	−0.858162	+	0.513379i	$0.828394\pi$
$440$			335188.i			0.0825385i
$441$	5.40455e6			1.32331
$442$			3.63425e6i			0.884830i
$443$	−5.66484e6			−1.37144			−0.685722	−	0.727863i	$-0.740513\pi$
$443$	−5.66484e6			−1.37144			−0.685722	+	0.727863i	$0.740513\pi$
$444$		−	547798.i		−	0.131875i
$445$	−3.39841e6			−0.813534
$446$		−	1.00489e7i		−	2.39211i
$447$	−262033.			−0.0620279
$448$	−8.98857e6			−2.11590
$449$	−877408.			−0.205393			−0.102697	−	0.994713i	$-0.532747\pi$
$449$	−877408.			−0.205393			−0.102697	+	0.994713i	$0.532747\pi$
$450$		−	4.90089e6i		−	1.14089i
$451$			1.54391e6i			0.357420i
$452$		−	7.59486e6i		−	1.74853i
$453$	314416.			0.0719880
$454$	6.43266e6			1.46471
$455$	5.28676e6			1.19718
$456$	−65314.5			−0.0147095
$457$	6.70015e6			1.50070			0.750350	−	0.661040i	$-0.229885\pi$
$457$	6.70015e6			1.50070			0.750350	+	0.661040i	$0.229885\pi$
$458$	−7.91755e6			−1.76371
$459$	−222993.			−0.0494037
$460$		−	848679.i		−	0.187003i
$461$			6.33978e6i			1.38938i	0.719308	+	0.694691i	$0.244459\pi$
$461$			6.33978e6i			1.38938i	−0.719308	+	0.694691i	$0.755541\pi$
$462$			365273.i			0.0796182i
$463$		−	5.29500e6i		−	1.14792i	−0.818882	−	0.573962i	$-0.805406\pi$
$463$		−	5.29500e6i		−	1.14792i	0.818882	−	0.573962i	$-0.194594\pi$
$464$	−1.63476e6			−0.352499
$465$			235538.i			0.0505159i
$466$			1.02445e7i			2.18538i
$467$		−	152809.i		−	0.0324233i	−0.999869	−	0.0162117i	$-0.994839\pi$
$467$		−	152809.i		−	0.0324233i	0.999869	−	0.0162117i	$-0.00516056\pi$
$468$		−	9.41200e6i		−	1.98640i
$469$		−	829116.i		−	0.174054i
$470$	4.06722e6			0.849283
$471$		−	6893.96i		−	0.00143191i
$472$			644010.i			0.133057i
$473$			2.19551e6i			0.451215i
$474$		−	379281.i		−	0.0775380i
$475$	2.44795e6			0.497815
$476$			3.35975e6i			0.679658i
$477$	8.36664e6			1.68366
$478$			7.62458e6i			1.52632i
$479$	−6.59570e6			−1.31348			−0.656738	−	0.754119i	$-0.728064\pi$
$479$	−6.59570e6			−1.31348			−0.656738	+	0.754119i	$0.728064\pi$
$480$		−	234041.i		−	0.0463648i
$481$			1.31034e7i			2.58238i
$482$	−5.11497e6			−1.00282
$483$		−	169142.i		−	0.0329901i
$484$	−4.64019e6			−0.900373
$485$			2.29116e6i			0.442283i
$486$	1.57531e6			0.302535
$487$	9.39884e6			1.79577			0.897887	−	0.440225i	$-0.145101\pi$
$487$	9.39884e6			1.79577			0.897887	+	0.440225i	$0.145101\pi$
$488$		−	2.36101e6i		−	0.448795i
$489$		−	89867.7i		−	0.0169954i
$490$	5.06857e6			0.953664
$491$	5.23373e6			0.979732			0.489866	−	0.871798i	$-0.337046\pi$
$491$	5.23373e6			0.979732			0.489866	+	0.871798i	$0.337046\pi$
$492$			310855.i			0.0578956i
$493$			953305.i			0.176650i
$494$	8.54263e6			1.57498
$495$	1.34186e6			0.246147
$496$			6.13991e6i			1.12062i
$497$		−	5.79439e6i		−	1.05224i
$498$	7624.03			0.00137756
$499$	−1.98530e6			−0.356922			−0.178461	−	0.983947i	$-0.557112\pi$
$499$	−1.98530e6			−0.356922			−0.178461	+	0.983947i	$0.557112\pi$
$500$		−	5.82027e6i		−	1.04116i
$501$	49161.0			0.00875038
$502$			1.40350e7i			2.48573i
$503$	6.32669e6			1.11495			0.557477	−	0.830193i	$-0.311770\pi$
$503$	6.32669e6			1.11495			0.557477	+	0.830193i	$0.311770\pi$
$504$		−	2.89159e6i		−	0.507061i
$505$		−	556316.i		−	0.0970719i
$506$	−1.40260e6			−0.243532
$507$		−	653398.i		−	0.112891i
$508$	−1.01884e7			−1.75166
$509$		−	7.74394e6i		−	1.32485i	−0.749127	−	0.662426i	$-0.769527\pi$
$509$		−	7.74394e6i		−	1.32485i	0.749127	−	0.662426i	$-0.230473\pi$
$510$	−104323.			−0.0177604
$511$			2.82656e6i			0.478856i
$512$		−	7.53839e6i		−	1.27088i
$513$			524164.i			0.0879374i
$514$		−	8.22076e6i		−	1.37247i
$515$	−2.25861e6			−0.375251
$516$			442052.i			0.0730885i
$517$		−	3.69917e6i		−	0.608665i
$518$			2.20119e7i			3.60440i
$519$			206482.i			0.0336484i
$520$		−	1.61431e6i		−	0.261806i
$521$	−8.04951e6			−1.29920			−0.649599	−	0.760277i	$-0.725063\pi$
$521$	−8.04951e6			−1.29920			−0.649599	+	0.760277i	$0.725063\pi$
$522$		−	4.48622e6i		−	0.720617i
$523$		−	9.44676e6i		−	1.51018i	−0.655622	−	0.755090i	$-0.727593\pi$
$523$		−	9.44676e6i		−	1.51018i	0.655622	−	0.755090i	$-0.272407\pi$
$524$			6.53687e6i			1.04002i
$525$		−	504112.i		−	0.0798232i
$526$	−1.74467e7			−2.74946
$527$	3.58047e6			0.561583
$528$	−162707.			−0.0253993
$529$	−5.78686e6			−0.899091
$530$	7.84652e6			1.21335
$531$	2.57817e6			0.396803
$532$	7.89739e6			1.20978
$533$		−	7.43567e6i		−	1.13371i
$534$			1.13084e6i			0.171613i
$535$		−	369959.i		−	0.0558816i
$536$	−253171.			−0.0380629
$537$	268200.			0.0401350
$538$	−2.85784e6			−0.425679
$539$		−	4.60992e6i		−	0.683473i
$540$	541606.			0.0799280
$541$		−	1.21038e7i		−	1.77799i	−0.457915	−	0.888996i	$-0.651403\pi$
$541$		−	1.21038e7i		−	1.77799i	0.457915	−	0.888996i	$-0.348597\pi$
$542$	1.60239e7			2.34299
$543$			286605.i			0.0417142i
$544$	−3.55772e6			−0.515435
$545$			1.88575e6i			0.271953i
$546$		−	1.75921e6i		−	0.252543i
$547$		−	8.84009e6i		−	1.26325i	−0.775275	−	0.631623i	$-0.782389\pi$
$547$		−	8.84009e6i		−	1.26325i	0.775275	−	0.631623i	$-0.217611\pi$
$548$	−9.25981e6			−1.31720
$549$	−9.45185e6			−1.33840
$550$	−4.18031e6			−0.589253
$551$	2.24083e6			0.314434
$552$	−51647.6			−0.00721444
$553$			8.38716e6i			1.16628i
$554$	−377796.			−0.0522977
$555$	−376136.			−0.0518338
$556$		−	1.20231e7i		−	1.64942i
$557$	4.52169e6			0.617536			0.308768	−	0.951137i	$-0.400083\pi$
$557$	4.52169e6			0.617536			0.308768	+	0.951137i	$0.400083\pi$
$558$	−1.68496e7			−2.29089
$559$		−	1.05739e7i		−	1.43122i
$560$			3.95598e6i			0.533069i
$561$			94882.4i			0.0127285i
$562$	7.62411e6			1.01824
$563$	653713.			0.0869193			0.0434597	−	0.999055i	$-0.486162\pi$
$563$	653713.			0.0869193			0.0434597	+	0.999055i	$0.486162\pi$
$564$		−	744804.i		−	0.0985926i
$565$	−5.21488e6			−0.687264
$566$	1.07195e7			1.40648
$567$	−1.15218e7			−1.50509
$568$	−1.76932e6			−0.230110
$569$	9.32108e6			1.20694			0.603470	−	0.797386i	$-0.293784\pi$
$569$	9.32108e6			1.20694			0.603470	+	0.797386i	$0.293784\pi$
$570$			245219.i			0.0316131i
$571$		−	1.06808e7i		−	1.37092i	−0.728108	−	0.685462i	$-0.759600\pi$
$571$		−	1.06808e7i		−	1.37092i	0.728108	−	0.685462i	$-0.240400\pi$
$572$	−8.02815e6			−1.02595
$573$			373171.i			0.0474812i
$574$		−	1.24909e7i		−	1.58240i
$575$	1.93572e6			0.244159
$576$	1.09877e7			1.37991
$577$			1.22061e7i			1.52629i	0.646230	+	0.763143i	$0.276345\pi$
$577$			1.22061e7i			1.52629i	−0.646230	+	0.763143i	$0.723655\pi$
$578$		−	1.03918e7i		−	1.29381i
$579$		−	658899.i		−	0.0816813i
$580$		−	2.31539e6i		−	0.285795i
$581$	−168593.			−0.0207204
$582$	762398.			0.0932984
$583$		−	7.13649e6i		−	0.869588i
$584$	863089.			0.104719
$585$	−6.46259e6			−0.780759
$586$			3.84019e6i			0.461965i
$587$	1.49764e7			1.79395			0.896977	−	0.442077i	$-0.145758\pi$
$587$	1.49764e7			1.79395			0.896977	+	0.442077i	$0.145758\pi$
$588$		−	928176.i		−	0.110710i
$589$		−	8.41622e6i		−	0.999605i
$590$	2.41790e6			0.285962
$591$	545492.	−	190432.i	0.0642421	−	0.0224270i
$592$	−9.80498e6			−1.14985
$593$			9.18814e6i			1.07298i	0.843907	+	0.536489i	$0.180250\pi$
$593$			9.18814e6i			1.07298i	−0.843907	+	0.536489i	$0.819750\pi$
$594$		−	895104.i		−	0.104090i
$595$	2.30692e6			0.267141
$596$		−	9.67450e6i		−	1.11561i
$597$	−520764.			−0.0598006
$598$	6.75511e6			0.772466
$599$		−	1.40003e7i		−	1.59430i	−0.603782	−	0.797149i	$-0.706340\pi$
$599$		−	1.40003e7i		−	1.59430i	0.603782	−	0.797149i	$-0.293660\pi$
$600$	−153931.			−0.0174561
$601$	−1.24915e7			−1.41068			−0.705338	−	0.708871i	$-0.749205\pi$
$601$	−1.24915e7			−1.41068			−0.705338	+	0.708871i	$0.749205\pi$
$602$		−	1.77627e7i		−	1.99765i
$603$			1.01352e6i			0.113511i
$604$			1.16085e7i			1.29475i
$605$			3.18611e6i			0.353893i
$606$	−185118.			−0.0204771
$607$	7.79634e6			0.858853			0.429427	−	0.903102i	$-0.358716\pi$
$607$	7.79634e6			0.858853			0.429427	+	0.903102i	$0.358716\pi$
$608$			8.36272e6i			0.917464i
$609$		−	461459.i		−	0.0504185i
$610$	−8.86427e6			−0.964536
$611$			1.78158e7i			1.93064i
$612$		−	4.10700e6i		−	0.443247i
$613$	1.71450e6			0.184283			0.0921416	−	0.995746i	$-0.470629\pi$
$613$	1.71450e6			0.184283			0.0921416	+	0.995746i	$0.470629\pi$
$614$	−7.47304e6			−0.799974
$615$	213444.			0.0227560
$616$	−2.46644e6			−0.261889
$617$	7.37154e6			0.779552			0.389776	−	0.920910i	$-0.372552\pi$
$617$	7.37154e6			0.779552			0.389776	+	0.920910i	$0.372552\pi$
$618$			751567.i			0.0791583i
$619$	−1.03932e6			−0.109024			−0.0545121	−	0.998513i	$-0.517360\pi$
$619$	−1.03932e6			−0.109024			−0.0545121	+	0.998513i	$0.517360\pi$
$620$	−8.69627e6			−0.908561
$621$			414484.i			0.0431300i
$622$			5.15606e6i			0.534370i
$623$		−	2.50067e7i		−	2.58129i
$624$	783622.			0.0805647
$625$	3.50962e6			0.359385
$626$			1.60544e7i			1.63741i
$627$	223029.			0.0226565
$628$	254531.			0.0257538
$629$			5.71775e6i			0.576234i
$630$	−1.08563e7			−1.08976
$631$	−1.78634e6			−0.178603			−0.0893017	−	0.996005i	$-0.528464\pi$
$631$	−1.78634e6			−0.178603			−0.0893017	+	0.996005i	$0.528464\pi$
$632$	2.56102e6			0.255047
$633$	−1.00264e6			−0.0994567
$634$	−2.82245e7			−2.78871
$635$			6.99573e6i			0.688492i
$636$		−	1.43689e6i		−	0.140857i
$637$			2.22020e7i			2.16792i
$638$	−3.82661e6			−0.372188
$639$			7.08313e6i			0.686235i
$640$	3.24397e6			0.313060
$641$			2.87273e6i			0.276153i	0.990422	+	0.138076i	$0.0440920\pi$
$641$			2.87273e6i			0.276153i	−0.990422	+	0.138076i	$0.955908\pi$
$642$	−123106.			−0.0117881
$643$		−	1.01506e7i		−	0.968198i	−0.875013	−	0.484099i	$-0.839147\pi$
$643$		−	1.01506e7i		−	0.968198i	0.875013	−	0.484099i	$-0.160853\pi$
$644$	6.24489e6			0.593349
$645$	303528.			0.0287276
$646$	3.72764e6			0.351441
$647$		−	1.25442e7i		−	1.17810i	−0.808098	−	0.589048i	$-0.799503\pi$
$647$		−	1.25442e7i		−	1.17810i	0.808098	−	0.589048i	$-0.200497\pi$
$648$			3.51819e6i			0.329141i
$649$		−	2.19910e6i		−	0.204943i
$650$	2.01330e7			1.86907
$651$	−1.73317e6			−0.160284
$652$	3.31800e6			0.305673
$653$	−5.00418e6			−0.459251			−0.229625	−	0.973279i	$-0.573750\pi$
$653$	−5.00418e6			−0.459251			−0.229625	+	0.973279i	$0.573750\pi$
$654$	627497.			0.0573677
$655$	4.48843e6			0.408782
$656$	5.56397e6			0.504806
$657$		−	3.45521e6i		−	0.312292i
$658$			2.99281e7i			2.69472i
$659$			1.35571e7i			1.21606i	0.793915	+	0.608029i	$0.208040\pi$
$659$			1.35571e7i			1.21606i	−0.793915	+	0.608029i	$0.791960\pi$
$660$		−	230451.i		−	0.0205929i
$661$	1.30874e7			1.16507			0.582534	−	0.812806i	$-0.302061\pi$
$661$	1.30874e7			1.16507			0.582534	+	0.812806i	$0.302061\pi$
$662$			4.99191e6i			0.442713i
$663$		−	456967.i		−	0.0403740i
$664$			51479.8i			0.00453124i
$665$		−	5.42261e6i		−	0.475504i
$666$		−	2.69076e7i		−	2.35065i
$667$	1.77194e6			0.154218
$668$			1.81507e6i			0.157381i
$669$			1.26354e6i			0.109150i
$670$			950514.i			0.0818034i
$671$			8.06214e6i			0.691264i
$672$	1.72216e6			0.147113
$673$			1.06900e6i			0.0909791i	0.998965	+	0.0454896i	$0.0144848\pi$
$673$			1.06900e6i			0.0909791i	−0.998965	+	0.0454896i	$0.985515\pi$
$674$	−1.68590e7			−1.42949
$675$			1.23533e6i			0.104358i
$676$	2.41241e7			2.03041
$677$		−	9.38306e6i		−	0.786815i	−0.919364	−	0.393408i	$-0.871296\pi$
$677$		−	9.38306e6i		−	0.786815i	0.919364	−	0.393408i	$-0.128704\pi$
$678$			1.73529e6i			0.144977i
$679$	−1.68592e7			−1.40334
$680$		−	704418.i		−	0.0584196i
$681$	−808836.			−0.0668333
$682$			1.43722e7i			1.18321i
$683$	−9.77752e6			−0.802004			−0.401002	−	0.916077i	$-0.631338\pi$
$683$	−9.77752e6			−0.802004			−0.401002	+	0.916077i	$0.631338\pi$
$684$	−9.65386e6			−0.788970
$685$			6.35809e6i			0.517726i
$686$			9.24281e6i			0.749884i
$687$	995544.			0.0804764
$688$	7.91224e6			0.637277
$689$			3.43704e7i			2.75827i
$690$			193908.i			0.0155050i
$691$	−1.42496e6			−0.113530			−0.0567648	−	0.998388i	$-0.518079\pi$
$691$	−1.42496e6			−0.113530			−0.0567648	+	0.998388i	$0.518079\pi$
$692$	−7.62353e6			−0.605188
$693$			9.87390e6i			0.781008i
$694$		−	541645.i		−	0.0426890i
$695$	−8.25548e6			−0.648306
$696$	−140907.			−0.0110258
$697$		−	3.24461e6i		−	0.252977i
$698$	−3.60632e6			−0.280173
$699$		−	1.28814e6i		−	0.0997170i
$700$	1.86123e7			1.43567
$701$		−	57588.4i		−	0.00442629i	−0.999998	−	0.00221315i	$-0.999296\pi$
$701$		−	57588.4i		−	0.00442629i	0.999998	−	0.00221315i	$-0.000704467\pi$
$702$			4.31095e6i			0.330164i
$703$	1.34401e7			1.02568
$704$		−	9.37219e6i		−	0.712705i
$705$	−511407.			−0.0387520
$706$		−	1.11953e7i		−	0.845329i
$707$	4.09358e6			0.308003
$708$		−	442775.i		−	0.0331971i
$709$		−	1.55758e7i		−	1.16368i	−0.813302	−	0.581842i	$-0.802332\pi$
$709$		−	1.55758e7i		−	1.16368i	0.813302	−	0.581842i	$-0.197668\pi$
$710$			6.64280e6i			0.494544i
$711$		−	1.02526e7i		−	0.760603i
$712$	−7.63581e6			−0.564489
$713$		−	6.65515e6i		−	0.490269i
$714$		−	767644.i		−	0.0563526i
$715$			5.51239e6i			0.403251i
$716$			9.90219e6i			0.721853i
$717$		−	958706.i		−	0.0696446i
$718$	2.34449e7			1.69722
$719$			2.27909e6i			0.164414i	0.996615	+	0.0822070i	$0.0261969\pi$
$719$			2.27909e6i			0.164414i	−0.996615	+	0.0822070i	$0.973803\pi$
$720$		−	4.83583e6i		−	0.347648i
$721$		−	1.66197e7i		−	1.19065i
$722$			1.21257e7i			0.865690i
$723$	643150.			0.0457580
$724$	−1.05817e7			−0.750256
$725$	5.28110e6			0.373146
$726$	1.06020e6			0.0746528
$727$	−1.63759e7			−1.14913			−0.574566	−	0.818458i	$-0.694829\pi$
$727$	−1.63759e7			−1.14913			−0.574566	+	0.818458i	$0.694829\pi$
$728$	1.18787e7			0.830694
$729$	1.39518e7			0.972327
$730$		−	3.24042e6i		−	0.225058i
$731$		−	4.61401e6i		−	0.319363i
$732$			1.62326e6i			0.111972i
$733$	3.18465e6			0.218928			0.109464	−	0.993991i	$-0.465087\pi$
$733$	3.18465e6			0.218928			0.109464	+	0.993991i	$0.465087\pi$
$734$	4.27941e7			2.93186
$735$	−637317.			−0.0435148
$736$			6.61285e6i			0.449981i
$737$	864502.			0.0586269
$738$			1.52690e7i			1.03198i
$739$	−2.87251e7			−1.93486			−0.967431	−	0.253134i	$-0.918539\pi$
$739$	−2.87251e7			−1.93486			−0.967431	+	0.253134i	$0.918539\pi$
$740$		−	1.38873e7i		−	0.932264i
$741$	−1.07414e6			−0.0718647
$742$			5.77376e7i			3.84990i
$743$			6.93623e6i			0.460948i	0.973079	+	0.230474i	$0.0740276\pi$
$743$			6.93623e6i			0.460948i	−0.973079	+	0.230474i	$0.925972\pi$
$744$			529225.i			0.0350516i
$745$	−6.64283e6			−0.438493
$746$	2.50380e7			1.64722
$747$	206090.			0.0135131
$748$	−3.50315e6			−0.228931
$749$	2.72229e6			0.177309
$750$			1.32983e6i			0.0863260i
$751$	−466943.			−0.0302109			−0.0151055	−	0.999886i	$-0.504808\pi$
$751$	−466943.			−0.0302109			−0.0151055	+	0.999886i	$0.504808\pi$
$752$	−1.33312e7			−0.859654
$753$		−	1.76475e6i		−	0.113421i
$754$	1.84295e7			1.18055
$755$	7.97082e6			0.508904
$756$			3.98534e6i			0.253607i
$757$		−	675222.i		−	0.0428259i	−0.999771	−	0.0214130i	$-0.993184\pi$
$757$		−	675222.i		−	0.0428259i	0.999771	−	0.0214130i	$-0.00681648\pi$
$758$		−	2.26518e6i		−	0.143195i
$759$	176361.			0.0111122
$760$	−1.65580e6			−0.103986
$761$			8.41071e6i			0.526467i	0.964732	+	0.263233i	$0.0847889\pi$
$761$			8.41071e6i			0.526467i	−0.964732	+	0.263233i	$0.915211\pi$
$762$	2.32788e6			0.145235
$763$	−1.38761e7			−0.862889
$764$	−1.37778e7			−0.853979
$765$	−2.82000e6			−0.174219
$766$	−4.46044e7			−2.74667
$767$			1.05912e7i			0.650065i
$768$			462464.i			0.0282927i
$769$	2.36177e7			1.44020			0.720099	−	0.693872i	$-0.244097\pi$
$769$	2.36177e7			1.44020			0.720099	+	0.693872i	$0.244097\pi$
$770$			9.26008e6i			0.562844i
$771$			1.03367e6i			0.0626247i
$772$	2.43272e7			1.46909
$773$	−9.72790e6			−0.585559			−0.292779	−	0.956180i	$-0.594580\pi$
$773$	−9.72790e6			−0.585559			−0.292779	+	0.956180i	$0.594580\pi$
$774$			2.17134e7i			1.30279i
$775$		−	1.98350e7i		−	1.18626i
$776$			5.14795e6i			0.306888i
$777$		−	2.76775e6i		−	0.164465i
$778$	−1.86852e7			−1.10675
$779$	−7.62675e6			−0.450294
$780$			1.10988e6i			0.0653193i
$781$	6.04169e6			0.354430
$782$	2.94765e6			0.172369
$783$			1.13081e6i			0.0659151i
$784$	−1.66133e7			−0.965309
$785$		−	174770.i		−	0.0101226i
$786$		−	1.49356e6i		−	0.0862314i
$787$	1.32044e7			0.759944			0.379972	−	0.924998i	$-0.375934\pi$
$787$	1.32044e7			0.759944			0.379972	+	0.924998i	$0.375934\pi$
$788$	7.03091e6	+	2.01401e7i	0.403363	+	1.15544i
$789$	2.19372e6			0.125455
$790$		−	9.61520e6i		−	0.548139i
$791$		−	3.83730e7i		−	2.18065i
$792$	3.01500e6			0.170795
$793$		−	3.88285e7i		−	2.19264i
$794$	−2.46695e6			−0.138870
$795$	−986614.			−0.0553642
$796$		−	1.92271e7i		−	1.07555i
$797$	−2.46843e6			−0.137649			−0.0688247	−	0.997629i	$-0.521925\pi$
$797$	−2.46843e6			−0.137649			−0.0688247	+	0.997629i	$0.521925\pi$
$798$	−1.80441e6			−0.100306
$799$			7.77404e6i			0.430804i
$800$			1.97090e7i			1.08878i
$801$			3.05685e7i			1.68342i
$802$			2.21753e7i			1.21740i
$803$	−2.94719e6			−0.161294
$804$	174062.			0.00949650
$805$		−	4.28795e6i		−	0.233217i
$806$		−	6.92186e7i		−	3.75306i
$807$	359342.			0.0194234
$808$		−	1.24998e6i		−	0.0673555i
$809$		−	7.38492e6i		−	0.396711i	−0.980130	−	0.198356i	$-0.936440\pi$
$809$		−	7.38492e6i		−	0.396711i	0.980130	−	0.198356i	$-0.0635601\pi$
$810$	1.32088e7			0.707378
$811$	2.04667e7			1.09269			0.546343	−	0.837561i	$-0.316019\pi$
$811$	2.04667e7			1.09269			0.546343	+	0.837561i	$0.316019\pi$
$812$	1.70375e7			0.906809
$813$	−2.01483e6			−0.106908
$814$	−2.29513e7			−1.21408
$815$		−	2.27825e6i		−	0.120145i
$816$	341939.			0.0179773
$817$	−1.08456e7			−0.568459
$818$			1.29277e7i			0.675521i
$819$		−	4.75541e7i		−	2.47730i
$820$			7.88054e6i			0.409281i
$821$	−3.53723e7			−1.83149			−0.915747	−	0.401756i	$-0.868400\pi$
$821$	−3.53723e7			−1.83149			−0.915747	+	0.401756i	$0.868400\pi$
$822$	2.11570e6			0.109213
$823$			2.92330e7i			1.50444i	0.658915	+	0.752218i	$0.271016\pi$
$823$			2.92330e7i			1.50444i	−0.658915	+	0.752218i	$0.728984\pi$
$824$	−5.07481e6			−0.260377
$825$	525627.			0.0268871
$826$			1.77918e7i			0.907338i
$827$	−4.94920e6			−0.251635			−0.125818	−	0.992053i	$-0.540155\pi$
$827$	−4.94920e6			−0.251635			−0.125818	+	0.992053i	$0.540155\pi$
$828$	−7.63382e6			−0.386960
$829$	−7.67098e6			−0.387672			−0.193836	−	0.981034i	$-0.562093\pi$
$829$	−7.67098e6			−0.387672			−0.193836	+	0.981034i	$0.562093\pi$
$830$	193278.			0.00973838
$831$	47503.6			0.00238630
$832$			4.51378e7i			2.26065i
$833$			9.68803e6i			0.483752i
$834$			2.74707e6i			0.136758i
$835$	1.24629e6			0.0618589
$836$			8.23445e6i			0.407492i
$837$	4.24716e6			0.209549
$838$			3.65566e7i			1.79827i
$839$	1.50539e7			0.738321			0.369161	−	0.929366i	$-0.379645\pi$
$839$	1.50539e7			0.738321			0.369161	+	0.929366i	$0.379645\pi$
$840$			340983.i			0.0166738i
$841$	−1.56769e7			−0.764311
$842$	−1.52090e7			−0.739300
$843$	−958648.			−0.0464612
$844$		−	3.70183e7i		−	1.78879i
$845$		−	1.65644e7i		−	0.798057i
$846$		−	3.65844e7i		−	1.75740i
$847$	−2.34446e7			−1.12288
$848$	−2.57187e7			−1.22817
$849$	−1.34786e6			−0.0641764
$850$	8.78518e6			0.417065
$851$	1.06278e7			0.503059
$852$	1.21645e6			0.0574112
$853$	−9.67263e6			−0.455168			−0.227584	−	0.973758i	$-0.573083\pi$
$853$	−9.67263e6			−0.455168			−0.227584	+	0.973758i	$0.573083\pi$
$854$		−	6.52266e7i		−	3.06041i
$855$			6.62866e6i			0.310106i
$856$		−	831253.i		−	0.0387747i
$857$			3.05784e7i			1.42221i	0.703088	+	0.711103i	$0.251804\pi$
$857$			3.05784e7i			1.42221i	−0.703088	+	0.711103i	$0.748196\pi$
$858$	1.83429e6			0.0850647
$859$			1.85013e7i			0.855497i	0.903898	+	0.427748i	$0.140693\pi$
$859$			1.85013e7i			0.855497i	−0.903898	+	0.427748i	$0.859307\pi$
$860$			1.12065e7i			0.516684i
$861$			1.57060e6i			0.0722032i
$862$		−	4.20688e7i		−	1.92838i
$863$		−	1.10711e7i		−	0.506014i	−0.967464	−	0.253007i	$-0.918580\pi$
$863$		−	1.10711e7i		−	0.506014i	0.967464	−	0.253007i	$-0.0814195\pi$
$864$	−4.22016e6			−0.192329
$865$			5.23457e6i			0.237870i
$866$		−	3.24379e6i		−	0.146980i
$867$			1.30665e6i			0.0590352i
$868$		−	6.39904e7i		−	2.88281i
$869$	−8.74512e6			−0.392841
$870$			529025.i			0.0236962i
$871$	−4.16357e6			−0.185960
$872$			4.23706e6i			0.188700i
$873$	2.06088e7			0.915203
$874$		−	6.92870e6i		−	0.306812i
$875$		−	2.94069e7i		−	1.29846i
$876$	−593397.			−0.0261268
$877$			2.45199e7i			1.07651i	0.842780	+	0.538257i	$0.180917\pi$
$877$			2.45199e7i			1.07651i	−0.842780	+	0.538257i	$0.819083\pi$
$878$	3.49747e7			1.53115
$879$		−	482862.i		−	0.0210790i
$880$	−4.12481e6			−0.179555
$881$	−1.48138e7			−0.643023			−0.321512	−	0.946906i	$-0.604191\pi$
$881$	−1.48138e7			−0.643023			−0.321512	+	0.946906i	$0.604191\pi$
$882$		−	4.55915e7i		−	1.97339i
$883$			5.36536e6i			0.231578i	0.993274	+	0.115789i	$0.0369396\pi$
$883$			5.36536e6i			0.231578i	−0.993274	+	0.115789i	$0.963060\pi$
$884$	1.68717e7			0.726151
$885$	−304024.			−0.0130482
$886$			4.77873e7i			2.04516i
$887$			6.54253e6i			0.279214i	0.990207	+	0.139607i	$0.0445838\pi$
$887$			6.54253e6i			0.279214i	−0.990207	+	0.139607i	$0.955416\pi$
$888$	−845133.			−0.0359660
$889$	−5.14771e7			−2.18454
$890$			2.86682e7i			1.21318i
$891$		−	1.20136e7i		−	0.506964i
$892$	−4.66511e7			−1.96313
$893$	1.82736e7			0.766822
$894$			2.21045e6i			0.0924989i
$895$	6.79917e6			0.283726
$896$			2.38704e7i			0.993319i
$897$	−849381.			−0.0352469
$898$			7.40162e6i			0.306292i
$899$		−	1.81568e7i		−	0.749273i
$900$	−2.27519e7			−0.936291
$901$			1.49978e7i			0.615482i
$902$	1.30240e7			0.533002
$903$			2.23347e6i			0.0911508i
$904$	−1.17172e7			−0.476874
$905$			7.26576e6i			0.294890i
$906$		−	2.65235e6i		−	0.107352i
$907$			1.66652e7i			0.672655i	0.941745	+	0.336327i	$0.109185\pi$
$907$			1.66652e7i			0.672655i	−0.941745	+	0.336327i	$0.890815\pi$
$908$		−	2.98630e7i		−	1.20204i
$909$	−5.00404e6			−0.200868
$910$		−	4.45979e7i		−	1.78530i
$911$		−	1.49127e7i		−	0.595334i	−0.954670	−	0.297667i	$-0.903791\pi$
$911$		−	1.49127e7i		−	0.595334i	0.954670	−	0.297667i	$-0.0962085\pi$
$912$		−	803758.i		−	0.0319991i
$913$		−	175788.i		−	0.00697931i
$914$		−	5.65209e7i		−	2.23792i
$915$	1.11458e6			0.0440109
$916$			3.67564e7i			1.44742i
$917$			3.30275e7i			1.29704i
$918$			1.88112e6i			0.0736731i
$919$			2.77410e7i			1.08351i	0.840536	+	0.541756i	$0.182240\pi$
$919$			2.77410e7i			1.08351i	−0.840536	+	0.541756i	$0.817760\pi$
$920$	−1.30933e6			−0.0510009
$921$	939652.			0.0365021
$922$	5.34809e7			2.07191
$923$	−2.90977e7			−1.12423
$924$	1.69574e6			0.0653401
$925$	3.16751e7			1.21720
$926$	−4.46674e7			−1.71184
$927$			2.03160e7i			0.776497i
$928$			1.80414e7i			0.687702i
$929$			2.94217e7i			1.11848i	0.829006	+	0.559240i	$0.188907\pi$
$929$			2.94217e7i			1.11848i	−0.829006	+	0.559240i	$0.811093\pi$
$930$	1.98694e6			0.0753317
$931$	2.27725e7			0.861068
$932$	4.75592e7			1.79347
$933$		−	648318.i		−	0.0243828i
$934$	−1.28906e6			−0.0483512
$935$			2.40538e6i			0.0899817i
$936$	−1.45207e7			−0.541748
$937$		−	4.70697e6i		−	0.175143i	−0.996158	−	0.0875715i	$-0.972089\pi$
$937$		−	4.70697e6i		−	0.175143i	0.996158	−	0.0875715i	$-0.0279106\pi$
$938$	−6.99423e6			−0.259557
$939$		−	2.01866e6i		−	0.0747135i
$940$		−	1.88816e7i		−	0.696979i
$941$			2.67296e6i			0.0984054i	0.998789	+	0.0492027i	$0.0156680\pi$
$941$			2.67296e6i			0.0984054i	−0.998789	+	0.0492027i	$0.984332\pi$
$942$	−58155.8			−0.00213534
$943$	−6.03087e6			−0.220852
$944$	−7.92518e6			−0.289454
$945$	2.73647e6			0.0996806
$946$	1.85208e7			0.672873
$947$			5.61298e6i			0.203385i	0.994816	+	0.101692i	$0.0324257\pi$
$947$			5.61298e6i			0.203385i	−0.994816	+	0.101692i	$0.967574\pi$
$948$	−1.76077e6			−0.0636330
$949$	1.41941e7			0.511614
$950$		−	2.06503e7i		−	0.742366i
$951$	3.54892e6			0.127246
$952$	5.18337e6			0.185362
$953$		−	2.67102e7i		−	0.952674i	−0.879263	−	0.476337i	$-0.841964\pi$
$953$		−	2.67102e7i		−	0.952674i	0.879263	−	0.476337i	$-0.158036\pi$
$954$		−	7.05791e7i		−	2.51076i
$955$			9.46031e6i			0.335658i
$956$	3.53963e7			1.25260
$957$	481154.			0.0169826
$958$			5.56398e7i			1.95872i
$959$	−4.67852e7			−1.64271
$960$	−1.29570e6			−0.0453759
$961$	−3.95651e7			−1.38199
$962$	1.10537e8			3.85097
$963$	−3.32776e6			−0.115634
$964$			2.37457e7i			0.822986i
$965$		−	1.67038e7i		−	0.577429i
$966$	−1.42685e6			−0.0491965
$967$		−	2.37511e7i		−	0.816805i	−0.912802	−	0.408402i	$-0.866086\pi$
$967$		−	2.37511e7i		−	0.816805i	0.912802	−	0.408402i	$-0.133914\pi$
$968$			7.15880e6i			0.245557i
$969$	−468710.			−0.0160359
$970$	1.93277e7			0.659553
$971$		−	1.81541e7i		−	0.617911i	−0.951076	−	0.308956i	$-0.900021\pi$
$971$		−	1.81541e7i		−	0.617911i	0.951076	−	0.308956i	$-0.0999794\pi$
$972$		−	7.31323e6i		−	0.248281i
$973$		−	6.07468e7i		−	2.05703i
$974$		−	7.92864e7i		−	2.67794i
$975$	−2.53150e6			−0.0852837
$976$	2.90546e7			0.976314
$977$			4.11447e7i			1.37904i	0.724265	+	0.689522i	$0.242179\pi$
$977$			4.11447e7i			1.37904i	−0.724265	+	0.689522i	$0.757821\pi$
$978$	−758104.			−0.0253444
$979$	2.60740e7			0.869463
$980$		−	2.35303e7i		−	0.782641i
$981$	1.69622e7			0.562744
$982$		−	4.41505e7i		−	1.46102i
$983$			2.57152e7i			0.848800i	0.905475	+	0.424400i	$0.139515\pi$
$983$			2.57152e7i			0.848800i	−0.905475	+	0.424400i	$0.860485\pi$
$984$	479582.			0.0157897
$985$	1.38289e7	−	4.82766e6i	0.454146	−	0.158543i
$986$	8.04186e6			0.263429
$987$		−	3.76312e6i		−	0.122958i
$988$		−	3.96583e7i		−	1.29253i
$989$	−8.57621e6			−0.278808
$990$		−	1.13196e7i		−	0.367066i
$991$	5.22978e6			0.169161			0.0845803	−	0.996417i	$-0.473045\pi$
$991$	5.22978e6			0.169161			0.0845803	+	0.996417i	$0.473045\pi$
$992$	6.77608e7			2.18625
$993$		−	627678.i		−	0.0202006i
$994$	−4.88802e7			−1.56916
$995$	−1.32020e7			−0.422748
$996$		−	35393.8i		−	0.00113052i
$997$			1.58014e7i			0.503453i	0.967798	+	0.251726i	$0.0809983\pi$
$997$			1.58014e7i			0.503453i	−0.967798	+	0.251726i	$0.919002\pi$
$998$			1.67475e7i			0.532260i
$999$			6.78239e6i			0.215015i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.6.b.a.196.13	✓	82
197.196	even	2	inner	197.6.b.a.196.70	yes	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.6.b.a.196.13	✓	82	1.1	even	1	trivial
197.6.b.a.196.70	yes	82	197.196	even	2	inner

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Groups

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	197.6.b.a.196.13

Level	$197$
Weight	$6$
Character	197.196
Analytic conductor	$31.596$
Analytic rank	$0$
Dimension	$82$
Inner twists	$2$